Abstract: Queue length distributions provide insight into the impact of service system design changes that go beyond simple performance measure averages; however, such distributions are difficult to estimate when service times are not exponential. In this research, we model service systems using queuing networks and develop a continuous time Markov chain (CTMC) to compute the steady state probability distribution function for the number of customers and the waiting time probabilities in a network of GI/G/c queues. Using a generalised generator matrix, we evaluate the steady state probability of any number of customers in the queue. For a network of general queues, we link the queues using a parametric decomposition approach. Through two service sector examples, we illustrate that explicitly modelling the arrival and service rates as general distributions (rather than approximating them using Markovian distributions) can lead to significantly better resource allocations.